Observations of Transiting Exoplanets with Differential Photometry

Brett Morris

*Note* - In the print publication, Figure 1 was appeared twice, including in place of Figure 2. This has been corrected here.

Abstract

Preliminary observations and computational methods for analysis are presented for observing celestial objects with time-varying intensity, in particular transiting exoplanets. Transits occur when a planet orbiting a star other than the sun (an exoplanet) passes between the Earth and the host star, slightly dimming the apparent intensity of the star. CCD images of the host star of one such exoplanet, HD 189733b, are recorded during predicted transits at the University of Maryland Observatory (UMO) on a small (152 mm) refracting telescope. Differential photometry algorithms compare the relative brightness of the host star to other nearby, non-variable stars in the field and detect the small change in brightness associated with a planetary transit, on the order of tens of millimagnitudes. The first successful exoplanet observations at UMO are presented and discussed, as well as possible implications for exoplanetary studies conducted by amateur and small observatories.

Introduction

Exoplanets are being discovered by the
hundreds today. The two principal methods of exoplanet detection involve: (a)
measuring the radial velocity of a star
for perturbations caused by a planet, or
(b) measuring the change in intensity of
a host star as a planet passes between the
star and Earth, known as a transit.

HD 189733b has been a favorable
exoplanet for transit observations since its
discovery by Bouchy et. al in 2005 [1]. It
orbits a nearby visual magnitude V=7.67,
K dwarf star with a period of 2.2 days
at a distance of 19.2 pc in the constellation Vulpecula [1,2]. The brightness of
the host star and its location - passing
through high altitudes in the summer sky
for observers in the northern hemisphere
-- make it an attractive target for small college observatories and serious amateurs.

Differential photometry is an observing technique used to compare the
relative changes in brightness between one
star and others nearby in the sky. An average is taken over the instrumental intensity
of a set of a few to many stars, called control stars, in CCD images over a period of time to account for changing atmospheric
conditions. The intensity measurements of
the star being analyzed for variation, called
the target star, are then corrected for the
atmospheric effects measured in the control stars, revealing its intrinsic variations.

Observations of transiting exoplanets are being collaboratively compiled and
compared by small college observatories
and skilled amateurs around the world [4].
Seagroves et al. (2003) argue that this class
of observers have distinct advantages to
offer for monitoring transiting exoplanets.
These advantages include diverse longitudinal locations, strength in numbers for
multiple simultaneous follow ups and lowcost observations [3]. Observatories in locations with bright light pollution and low
elevation can still prove useful in bright
transiting exoplanet observations.

Here I present the first observations of an exoplanet at the University of
Maryland Observatory, as well as an original differential photometry algorithm for
accessible transiting exoplanet detection
for college observatories and serious amateurs. The observing techniques and apparatus are detailed in the Observational
Methods section, the differential photometry algorithm is introduced in Analysis,
some observations are shown in Results
and discussed in the Discussion section.

Observational Methods

Apparatus: All observations discussed
here were taken with a 152mm Astro-Physics f/9 refracting telescope on an AP900
equatorial mount temporarily installed at
the University of Maryland Observatory
(UMO) in College Park, MD, US, located
<6 km from the District of Columbia at
an elevation of ~100 m above sea level.
Images were recorded on an SBIG ST-10
CCD camera with 6.8 square micron pixels in an array of dimensions 2184 x 1472.
The field of view was approximately 0.5°
x 0.75° with a focal reducer in place. The
CCD was cooled to -5 °C, controlled by
MaxIm DL (Version 5.12). The Baader RCCD red filter was used exclusively in the
presented observations.

Observing Techniques: Dark frames
are collected by exposing the CCD without sky illumination and recording the
background noise, hot pixels and thermal
noise, which is then subtracted from each
image of the sky. Flat fielding is performed
by exposing the CCD to light projected
evenly on a screen in the observatory. The
isotropic light field becomes attenuated by
dust and other imperfections in the optical
path of the telescope resulting in systematic variations in the flat field exposures.
Several of these exposures are averaged
and the resulting image is normalized by
the mean pixel intensity. All sky exposures
are divided by this "master flat."

A red filter was used for all photometric observations. A typical photometric event such as an exoplanet transit or
a short period pulsating variable star peak
event happens over the course of several
hours. The altitude of the object of interest can change greatly in that time leading to changing atmospheric extinction
throughout the night. This extinction also
varies with wavelength, affecting the longer wavelengths less than shorter ones.
Thus, the red filter was used to select the
light from any color star that is least affected by atmospheric extinction.

Defocusing the telescope is commonly used in differential photometry to
spread the light of a bright star over many
pixels. The greater imaging area covered
by the star reduces some systematic errors unaccounted for by the dark frames and
flat fields associated with focusing large
amounts of the light on individual pixels.
The decreased intensity of the light on
each individual pixel also allows for longer exposures without risk of saturation,
which can in effect smooth out some atmospheric noise that happens on short
time scales. Transit observations are presented here with and without defocusing.

After the CCD is cooled and dark
frames are exposed, the star of interest is
found and centered in the field of view.
The target star is centered to keep it in
the frame despite the imperfect tracking
of the telescope. The particular telescope
used here, like many others, is in slightly
off-polar alignment, causing stars to drift
in the field of view throughout the course
of a night. A favorable alignment keeps
the target star in the frame for as long as
possible while also orienting itself to maximize the number of control stars in the
frame for comparison. Exposure lengths
are adjusted so that the brightest control
stars are recording maximum pixel intensities significantly below saturation.

Analysis

A suite of differential photometry software named "oscaar" (for "Open Source
Differential Photometry Code for Amateur Astronomical Research") was developed in Python to generate light curves
from the series of images recorded by the
CCD. The code has several key phases of
analysis which will be discussed here in
some detail, namely star tracking, aperture
photometry, and differential comparison.
This section will discuss analysis of "stars"
or "objects" in general. These methods
can be used to observe exoplanet transits,
variable stars and rotating asteroids among
others.

The drift of the stars due to imperfect telescope tracking is a ubiquitous
obstacle to iterative measurement of star
magnitude in low-power observatories.
The problem of tracking object positions
becomes unavoidable for observations of
asteroids, for example, which can move
significantly with respect to the sky in a
few hours. Oscaar takes user input from
SAOImage DS9 to record approximate
centroid positions and radii of target and
control stars chosen by the user in the
first image in a photometry set. The explicit choice of objects by the user provides a check against unfavorable objects
for photometry. Gaussian functions are fit
to the intensities in the regions immediately around the object centroids using chi-squared
minimization. The coordinates of the object centroids and the s parameter corresponding to the radial spread of the object
are recorded and used as initial estimates in
the fit for the next frame. This method of
tracking is not affected by the independent
motion of one or more of the tracked objects.

The object centroids and radii provide the basis for the aperture photometry measurements. The source aperture
is centered on the fit centroid with radius
5.5σ where σ is again the Gaussian width
parameter from the fitting process. This
large factor of σ was chosen to loosely
enclose >99% of the source light even
in poor Gaussian fits. The sky aperture
has concentric radii 5.5σ to 7.5σ. The
median of the intensities in the sky aperture is interpreted as a measurement of
the background intensity of the sky. This
background value is subtracted from each
pixel intensity in the source aperture and
the resulting array is summed to derive the instrumental intensity of the object. The
instrumental magnitude is converted to
an astronomical magnitude. These calculations are summarized symbolically for
clarity in the Appendix.

The magnitude of the control stars
at each time is averaged into one aggregate control intensity measurement of
the variations of the stars throughout the
period of observation. The differential
photometric measurement of the variation in the target star is simply the magnitude of the target star subtracted from
this aggregate control intensity. A star with
no variability relative to the control stars
is represented by a function of constant
magnitude throughout time; objects with
variability show non-zero and time-varying slopes.

Oscaar is intended for small observatories and serious amateurs. It is
commanded by a user edited plain text
parameter file that controls the running
parameters of the algorithms and indicates the input files. Users need not interact with the underlying Python code to
generate light curves from raw CCD images, and a graphical user interface is provided to display the control and target star
differential magnitude light curves. A free
open source distribution of oscaar is available online.

Results

The first successful observation of an
exoplanet at UMO was produced in collaboration with UM undergraduate Harley Katz. A time series of images of HD
189733b and the surrounding star field
was collected during a predicted transit
[4]. Light curves demonstrating the diminished intensity of the star during the
transit were generated by oscaar using 25
bright comparison stars ranging in magnitude from about 8-12 magnitude. This
magnitude range is constrained by low signal from stars dimmer than 12 mag and
lack of stars above 8 mag. The telescope
was well-focused, necessitating short (7 s)
exposures. Over 190 minutes, 607 images
were collected. The resulting light curve
in Figure 1 shows a 28.3 +/- 0.5 mmag attenuation of the star light at the predicted
time of transit. The expected depth is 28.2
mmag [1].

Figure 1: The first successful exoplanet transit light curve from UMO.
The set of circles represent the magnitude of host star HD
189733. The set of x's represent the magnitude of a non-
variable control star, HIP 98523. The connected dark squares
represent 25 point median binning. The control data is given
a vertical displacement for clarity.

A second set of observations were collected using the defocusing method. The
light was effectively defocused by the extremely humid atmosphere in College
Park, which approached 94% humidity toward the end of the transit. The centroid
fitting routine produced a mean σ fit
parameter - corresponding to the radial
spread of each star - 30.5% larger in the
naturally defocused run than in the well-focused data set. The widely distributed
light decreased the peak intensity at stellar
centroids and enabled exposures to be increased to 20 s. 37 control stars were chosen for differential photometry, producing
the light curve in Figure 2.

Figure 3: Third photometric observation of HD 189733b, with intentional defocusing. The observed depth is 29.0 +/- 0.4 mmag. The connected dark squares represent 25 point median binning. The transit observation is incomplete due to poor weather at ingress.

The observations were repeated on a
night with 60% humidity (less optically
significant) and intentional defocusing of
the telescope components. The telescope
was focused on globular cluster M13 and
defocused such that the intensity of a typical star centroid decreased by a factor of
2.5 in the same exposure time. 28 control
stars were tracked in 337 frames with 12 s
exposures. The results shown in Figure 3
confirm the benefits of defocusing.

Discussion

The results confirm that exoplanet transit
light curves can be collected by small observatories in non-ideal locations. UMO
is well within the Washington, DC light
pollution "bubble," which is considered a
Bortle-scale 9 or 10 site [5]. College Park is
heavily populated, ~100 m above sea level and typically very humid. As discussed
in the Results section, a verified method
for defocusing can be to view the star on nights of high humidity (see Figure 2),
which successfully reduces noise in the
light curve. In the case of bright transiting exoplanet detection, atmospheric conditions that can otherwise be crippling to
astronomical research can benefit transit
observations.

Light pollution at UMO significantly increases the background sky intensity,
effectively making the signal-to-noise ratio
poorer for dim stars. The number of control stars available in a given field is therefore reduced due to the location of UMO.
There are still many viable control stars in
star fields as dense as the region surrounding HD 189733. The number of stars does
not significantly change the light curve in
a differential photometric observation of
>20 stars. This suggests that more sparse
star fields will still produce quality light
curves of bright transiting exoplanets at
small observatories.

The success of the defocusing technique can be attributed to several factors.
The increased exposure length compensates for the decreased intensity of the
brightest pixels in each frame. The longer
exposure length may be integrating over
a time cycle longer than the atmospheric
fluctuations that are a source of noise in
the shorter exposures. Defocusing also
provides a natural form of dithering. The
star light is spread out over more pixels,
lessening the significance of pixel-to-pixel
variations that may have eluded correction
in the dark frame and flat field processing.

The imperfect polar alignment of
the telescope may be a source of uncorrected systematic error. The target star
drifted ~275 pixels in the 2011 Jun 30
observation, which significantly spreads
the observation over many pixels. The
flat fielding normalization and dark frame
subtraction are assumed to remove any
systematic effects along the length of the
detector and some corrected images were
visually inspected to ensure the calibration
process successfully removed obvious systematic effects.

It has now been shown that small
college observatories like UMO can produce quality light curves of transiting
exoplanets. It should be noted that these
observations were recorded using standard college observatory apparatus, and
can likely be repeated in other small observatories. The quality of these observations is likely to increase as the observing
techniques are refined and preliminary ob-
servations of dimmer transiting exoplanets suggest that stars dimmer than HD
189733 by several magnitudes can be observed at UMO. Online transit predictions
by services like those of Poddany et al.
(2010) provide up-to-date ephemerides on
observable transiting exoplanets [4]. These
accurate predictions minimize observing
time for follow-up observations by allowing observers to plan observing sessions
to the minute. Poddany et al. (2010) also
provide a streamlined, centralized system
for updating these ephemerides with new
user collected data. The author plans to
monitor candidate transiting exoplanets
for follow-up observations to constrain
ephemerides, and to contribute to these
databases with the results that are collected.

Conclusions

Small observatories such as the University
of Maryland Observatory are capable of
recording light curves of bright transiting exoplanets such as HD 189733b with
common apparatus. Rather simple differential photometry algorithms can define
transits of reasonable quality with ~20
control stars.

Appendix

Presented here for clarity is a mathemati-
cal summary of the flat field normalization
and dark frame subtraction process ap-
plied to each aperture photometry source.
Given
{si} is the set of intensities of the source
pixels
{σi} is the set of intensities of the sky
(background) pixels
{di} is the set of intensities of the dark
frame
{fi} is a set of intensities of the flat field
(of which there are several),The set of the intensities of the normalized average of the flat fields {Fi} is given by:The instrumental magnitude of the star is then: And the differential astronomical magnitude is given by:

Acknowledgements

The author would like to thank Elizabeth Warner (UMCP), the Observatory
Coordinator, for providing access to the
facilities at the University of Maryland Observatory and training with the telescope.
Some of the observatory setup procedures
were completed with assistance from fellow undergraduate Harley Katz (UMCP)
on several occasions. This project was inspired by a conversation with Dr. David
Charbonneau (Harvard) and is being continued with Dr. Drake Deming (UMCP).